All points along the circle with be the distance of the radius from the center...so the radius can be found using the Pythagorean Theorem..
r^2=(4-1)^2+(6-2)^2
r^2=9+16
r^2=25
r=5
The equation of the circle can be expressed as:
r^2=(x-h)^2+(y-k)^2 where (h,k) correspond to the center of the circle, (2,1) in this case.
(x-2)^2+(y-1)^2=25
if you wanted it in a more standard form...
(y-1)^2=25-(x-2)^2
(y-1)^2=25-x^2+4x-4
(y-1)^2=-x^2+4x+21
y-1=(-x^2+4x+21)^(1/2)
y=1(+/-)(-x^2+4x+21)^(1/2)
Step-by-step explanation:
In a standard deck of 52 cards, there are 2 red aces, 2 red Queens, and 13 spades. That leaves 35 cards for everything else.
For the game to be fair, the cost must equal the expected value. The expected value is the sum of each outcome times its probability.
C = (12) (13/52) + (20) (2/52) + (38) (2/52) + (0) (35/52)
C = 68/13
C ≈ 5.2308
Answer:
Step-by-step explanation:
Given the matrices
Calculating AB:
Multiply the rows of the first matrix by the columns of the second matrix
Hence,
Therefore,
and the area would be 
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